public class FaureSequence extends Object implements Serializable, RandomSequence, Cloneable
Discrepancy measures the deviation from uniformity of a point set.
The discrepancy of the point set , is
where the supremum is over all subsets of of the form is the Lebesque measure, and A(E;n) is the number of the contained in E.The sequence of points in is a lowdiscrepancy sequence if there exists a constant c(d), depending only on d, such that
for all .Generalized Faure sequences can be defined for any prime base . The lowest bound for the discrepancy is obtained for the smallest prime , so the base defaults to the smallest prime greater than or equal to the dimension.
The generalized Faure sequence , is computed as follows:
Write the positive integer n in its bary expansion,
where are integers, .The jth coordinate of is
The generator matrix for the series, , is defined to be
and is an element of the Pascal matrix,It is faster to compute a shuffled Faure sequence than to compute the Faure sequence itself. It can be shown that this shuffling preserves the lowdiscrepancy property.
The shuffling used is the bary Gray code. The function G(n) maps the positive integer n into the integer given by its bary expansion. The sequence computed by this function is , where is the generalized Faure sequence.
Constructor and Description 

FaureSequence(int dim)
Creates a Faure sequence with the default base.

FaureSequence(int dim,
int base,
int nSkip)
Creates a Faure sequence.

Modifier and Type  Method and Description 

Object 
clone()
Returns a copy of this object.

int 
getBase()
Returns the base.

long 
getCount() 
int 
getDimension()
Returns the dimension of the sequence.

int 
getSkip()
Returns the number of points skipped at the beginning of the sequence.

double 
nextDouble()
Returns the first value of the next point in the sequence.

double[] 
nextPoint()
Returns the next point in the sequence.

static int 
nextPrime(int n)
Returns the smallest prime greater than or equal to n.

public FaureSequence(int dim)
dim
 is the dimension of the sequence.public FaureSequence(int dim, int base, int nSkip)
dim
 is the dimension of the sequence.base
 is the base of the sequence, as described above.
It must be at least as large as dim.nSkip
 is the number of initial points to skip.
If negative then ,
where m is the number of digits needed to represent
the Integer.MAX_VALUE
in the base,
points are skipped.public int getBase()
public long getCount()
public int getDimension()
getDimension
in interface RandomSequence
public int getSkip()
public double nextDouble()
double
array, the next sequence value.public double[] nextPoint()
nextPoint
in interface RandomSequence
double
array, the next point in the sequence.public static int nextPrime(int n)
n
 is the first number to try as a prime.Copyright © 19702015 Rogue Wave Software
Built October 13 2015.